1. Field of the Invention
This invention relates to a method for predicting an intrinsic property of a mixture comprising at least two components.
2. Background of the Invention
Gasoline blending is a complex process whose goal is a gasoline blend that meets a variety of environmental and contractual specifications, and has the lowest possible cost. Typically, from five to fifteen blend stocks are available for blending. Some of the components will have a high economic value because they meet many of the specifications and are difficult to produce, e.g., alkylate stocks. Others will have a low economic value because they do not meet specifications, but are relatively easy to produce. The availability and properties of the blend stocks vary with changes in refinery operation.
In order to accomplish this goal, it is desirable to have an accurate model to predict gasoline properties from the amounts and properties of the component blend stocks. If the model is inaccurate, one or more properties of the blended gasoline will differ from the prediction, and the blended gasoline may not meet specifications. In such a case, blending needs to be performed with a process control system which adjusts the amounts of the components during blending, or in some cases, the gasoline will need to be reblended with high-value components. Use of an accurate model could avoid these inefficiencies and might save millions of dollars over the course of a year.
The simplest type of blend model is the linear model, which has the following form: ##EQU1## where y is the property of the blend, m is the number of components in the blend, c.sub.i is the volume fraction of the i.sup.th component and b.sub.i is the model coefficient for the i.sup.th component. The coefficients are sometimes referred to as the neat values because if the blend recipe is simply a pure component, i.e., c.sub.i =1 and all other c's are 0, then the predicted property is equal to the coefficient for the component. The linear model assumes that the blend property is a flat surface between the values of the pure compounds. This will be true in an ideal system having no interactions between the components. To the extent that this assumption is incorrect there is a difference between the true property and the prediction of the linear model. An example of a linear blend model is described in U.S. Pat. No. 5,475,612 to Espinosa. Properties for a blend of hydrocarbon components are predicted using a linear equation. Each term in the equation is the product of a quantity derived from a near-infrared spectroscopy (NIR) measurement of a component and the volume fraction of that component. The NIR measurements are performed only on single components, with no data obtained from mixtures of components. In addition, no interaction terms are used in the blend model equation. This method cannot account for non-additive effects on mixture properties caused by interactions between components.
An approach to modeling blend systems in which there is a significant interaction between the components is the interaction model. A binary interaction model includes terms which account for pair-wise interactions between components, and has the following form: ##EQU2## The first term in this equation is equivalent to the linear model and the second term is a non-linear term to account for the curvature present in the actual property surface. The b.sub.i coefficients are the linear terms and the b.sub.ij coefficients are the binary interaction terms. Higher-order interaction terms which comprise a coefficient and the product of three or more concentrations can be added to the model, but are typically not significant.
Use of the binary interaction model to predict octane values in blended gasoline is described in W. E. Morris, Oil & Gas Journal, Jan. 20, 1986. Morris suggests that all coefficients be determined by actual measurements of pure components or blends. The linear b.sub.i coefficients are then automatically equal to the property of the pure i.sup.th component. Morris determines of the interaction coefficients by measuring octane values for a 50:50 blend of each pair of components in addition to the pure components.
Application of the method suggested by Morris requires determination of a large number of property values, which may need to be repeated as the composition of blend components changes. For example, application of the interaction model to predict octane number for a mixture often gasoline feed stocks requires analysis of 55 samples in a knock engine, a time-consuming procedure. Alternatively, libraries of octane interaction values are available in the literature. An obvious problem with using literature values is that a particular blending stock may be very different, depending on location and time of production.
Another problem with actual property measurements on neat components and 50:50 blends is that the neat and 50:50 blend samples used to determine the interaction coefficients are extreme samples. There are no practical gasoline blends with compositions that are close to these values. Thus, coefficients derived from such samples will not reliably predict properties of actual gasoline blends. Another consequence of the extreme nature of these samples is that accurate measurement of some properties, e.g., octane values, will not be possible for some components and mixtures having large amounts of components with high vapor pressures, e.g., butane and light cracked gas.
Actual property measurements on more realistic samples tend to be inaccurate due to errors in volume measurement of components present at low concentrations. Such errors are exacerbated because the difficulty of performing actual property measurements leads to measurement of only a small number of samples, which does not allow averaging of errors.